Hadley article on parity: physics/0406118

[CarlB]

Any comments on this pithy article on parity:

A Conserved Parity Operator
Mark J. Hadley, Dept of Phys., Univ. of Warwick,

Abstract:The symmetry of Nature under a Space Inversion is described by a Parity operator. Contrary to popular belief, the Parity operator is not unique. The choice of the Parity operator requires several arbitrary decisions to be made. It is shown that alternative, equally plausible, choices leads to the definition of a Parity operator that is conserved by the Weak Interactions. The operator commonly known as CP is a more appropriate choice for a Parity operator.
...
Maxwell’s equations have an Electric Field, E, and a Magnetic field, B. A simple mathematical representation would be to treat them both as vectors. Both E and B would then change sign under a parity operation. Maxwell’s equation would not be invariant under this parity operation.
...
Electrodynamics would be inherently lefthanded. A symmetrical experimental arrangement such as an electron beam moving forward in the x-direction and a magnetic field pointing in the z-direction would result in electrons moving to the left. The mirror image would be contrary to experimental observations.
...
Without a deeper model of the elementary particles and their quantum numbers, the assignment of their transformation properties is only a matter of aesthetics. However the motivation for this analysis came from just such models. The author is working on geometric models of elementary particles and quantum theory using classical general relativity [6, 7]. Some exciting results have been achieved (see for example [8]), but a clear prediction of such models is that parity is conserved. ...
http://arxiv.org/abs/physics/0406118

Carl

 

[Hans de Vries]

...
Maxwell’s equations have an Electric Field, E, and a Magnetic field, B. A simple mathematical representation would be to treat them both as vectors. Both E and B would then change sign under a parity operation. Maxwell’s equation would not be invariant under this parity operation.
...
http://arxiv.org/abs/physics/0406118

Carl

I'm quite happy to view the Magnetic field B as a relativistic side effect of
the Electric field E. I've been looking into this for a while. It fits very nicely
within the Lienard Wiechert framework.

The Maxwell picture of almost complete symmetry between E and B has
it short comings and B not transforming like a vector is a very important
one.

I can imagine that the magnetic monopole people (Jay Yablon did also
some very interesting work recently) would love to redefine the definition
of parity in order to improve E B symmetry I personally regard
monopoles as not so likely just because of this relativistic relationship.

The whole EM field can be described by only two scalar values and their
derivatives instead of the six scalars needed for E and B ( e.g. Lewis H. Ryder
paragraph 3.3) An interesting question would be if that still holds if there
are monopoles (depending on the type of monopole, Dirac, 't Hooft-Polyakov,
Jay's theory ).



Regards, Hans.


P.S: One should warn that some popular texts erroneously use a bizarre
"splitting wire" argument to derive the required gamma factor needed in the
proof that the Magnetic field is a relativistic side effect of the Electric field :

A wire carrying a current splits into two different ones of different length,
one being the electrons and one being the positive charges. The naive
argument is that both have different (average) speeds and thus different
Lorentz contractions... Neutrality is last because of the different charge
densities and the test-charge feels a net force.

The correct way to obtain the gamma is by using Lienard Wiechert as shown
by Emil Wiechert in 1900 (well before Einstein's famous year 1905).

 

[CarlB]

I'm quite happy to view the Magnetic field B as a relativistic side effect of the Electric field E. I've been looking into this for a while. It fits very nicely within the Lienard Wiechert framework. ... The whole EM field can be described by only two scalar values and their derivatives instead of the six scalars needed for E and B ( e.g. Lewis H. Ryder
paragraph 3.3)

I like the Lienard Wiechert framework becomes it fits into my understanding of the primacy of the sources, as in Schwinger's source theory, rather than the gauge fields. And anything that can reduce the number of unphysical degrees of freedom is likely to be an improvement.

I wonder what the effect of translating the Aharonov-Bohm effect into Lienard-Wiechert terms would be. That is, it seems to me that the split method where one separates the + and - charge carriers (in the solenoid that sits between the particle slits) seems appropriate for this instance. That is, one must sum the QED interaction over the moving and nonmoving charges in order to compute the correction for the quantum interference. When the problem is done the usual way, one obtains a gauge freedom for the magnetic potential that evidently won't exist in the Lienard-Wiechert calculation. Comments?

Carl

By the way, it's a small world. While looking up the "Lienard Wiechert" framework, I found a paper that, like my own efforts, upgrades proper time from being just a parameter to being an element of the manifold:

http://www.arxiv.org/PS_cache/physics/pdf/0302/0302006.pdf

though I think my version is a lot more elegant and applicable to particles.

 

[Hans de Vries]

I wonder what the effect of translating the Aharonov-Bohm effect into Lienard-Wiechert terms would be. That is, it seems to me that the split method where one separates the + and - charge carriers (in the solenoid that sits between the particle slits) seems appropriate for this instance. That is, one must sum the QED interaction over the moving and nonmoving charges in order to compute the correction for the quantum interference. When the problem is done the usual way, one obtains a gauge freedom for the magnetic potential that evidently won't exist in the Lienard-Wiechert calculation. Comments?

Lienard-Wiechert showed long before QM that the potentials are the
fundamental entities with the fields being only the derivatives (literally).
There's no freedom to do gauge type mathematical manipulations with
the potentials in Lienard-Wiechert.

One of the basic things that still bothers me with this subject is that
we don't see more of the electric Aharonov-Bohm effect, basically
expressed by the $\mu_0$ term in the covariant derivative:

$$\def\pds{\kern+0.1em /\kern-0.55em \partial} \def\lts#1{\kern+0.1em /\kern-0.65em #1} \lts{D}_\mu \ \equiv\ \pds_\mu + ieA_\mu$$

For instance in a rather basic situation like AC power transmission lines.
The highest voltage in commercial AC power lines is 1.15 MV which cycles
over a voltage range significantly higher than the electrons rest-mass...

(http://205.243.100.155/frames/longarc.htm)

As far as I know the electric Aharonov-Bohm effect has only be tested in
a much less straight forward experiment here:

http://web.mit.edu/biophysics/papers/NATURE1998.pdf

which looks for an interference pattern between electrons and holes(!) in
a semiconductor consisting out of two half arcs, one for the holes and one
for the electrons. This requires a "positive charge, negative mass" hole
which is different from a "positive charge, positive mass" positron.

In the latter case we should get the phase difference according to the sum
of the potentials instead of the difference of the potentials. If you forget
about the hole and consider an assembly of electrons with one missing then
you need coherence between all the electrons in the hole arc.

I have no problem to just interfere the electrostatic Aharonov-Bohm effect
from the magnetic one via SR though but this still keeps puzzling me.Regards, Hans

 

[CarlB]

One of the basic things that still bothers me with this subject is that we don't see more of the electric Aharonov-Bohm effect, basically expressed by the $\mu_0$ term in the covariant derivative:

I recall that the Sakurai "Modern Quantum Mechanics" textbook gives has the example of the electric A-B effect rather than the usual one. According to Amazon, it would be in section 2.6, "Potentials and gauge transformations".

By the way, I picked up a used copy of a quark and lepton primer that is being used as a text at the University of New Mexico (Albuquerque, NM, USA). It's by Halzen and Martin called "Quarks and Leptons: An Introductory Course in Modern Particle Physics". So far it seems like a wonderful introductory book.

Carl

 

[Hans de Vries]

I recall that the Sakurai "Modern Quantum Mechanics" textbook gives has the example of the electric A-B effect rather than the usual one. According to Amazon, it would be in section 2.6, "Potentials and gauge transformations".
Carl

I do like Sakurai "Modern Quantum Mechanics", but ufortunately it is almost
completely non-relativistic.The point is that I want to be able to close my eyes and see all these
things in front of me. Do Lorentz transforms on Quantum Mechanical scenes
including vector potentials and see all the phases in front of me, and in the
end see how local differences in phase(-rates) corresponds to accelaration.
(identifying the forces) Ok. It's evident that the absolute potential shouldn't influence observable
physics. that's not the point. The mentioned voltage of the AC power line
of 1.15 MV is probable nothing compared to what happens at astronomical
scales.

So you can't do without a global gauge invariance of $e^{i\alpha t}$, OK. but then
SR will transform that to a gauge invariance of $e^{i\beta x}$, which however is not
allowed to influence any interference patterns.

It doesn't do so indeed if you map this phase change over the whole scene
completely independent of the momentum (direction) en energy of any wave-
functions. This for instance does force the elementary charge e to be exactly
constant otherwise different phase changes over different paths would lead
to interference effects.

A local variation of the charge e of say 10^-15 should give clearly observable
effects with the electrons rest frequency of ~10²⁰ Hz in a potential field
which exceeds the electrons rest mass.

So the term $ieA_\mu \phi$ should also be completely independent of the energy
/momentum of the particle, which off course it is, because this would again
lead to interference effects. I'm always missing these kind of remarks in
textbooks needed to give you some true insight.Regards, HansP.S. So I’ve got no problem with the picture above but there is a conflict
with quite common ideas like: The mass of a charged particle decreases in
a potential well (e.g. nuclear fusion) The idea that an electron and positron
approaching each other loose more and more mass the deeper the get in
the potential wells until they end up as mass less photons.

The whole concept of electromagnetic mass doesn’t fit well in the picture
above. The energies of the fields must be viewed separated from the masses
of the particles altough the combined mass (energy) has a meaning.

 

[CarlB]

A question about the scalar potentials of Lienard-Wiechert. What are the two scalar values that can be used, along with their derivatives, to describe E&M fields? Or can this be done for only one source point charge at a time?

Carl

P.S. I believe that classical mass is a measure of the energy in the wave in the hidden proper time direction. With that point of view, there is no need to wonder about how bound particles can cancel mass, but it's not a popular point of view.

The principle that bound particles can cancel mass becomes more and more important the more fundamental you chase the physics. It is negligible in chemical bound states, becomes more important at fission and fusion bound states, and when one supposes that the quarks and leptons are bound states of subparticles the cancellation of mass becomes supremely important.

Which reminds me. The fine structure constant, 1/137, is defined with respect to the electron. If the electron became much heavier with no change to its electric charge, the fine structure constant would become even smaller. Getting back to the Koide mass formula, this says that if you consider the natural charged lepton mass to be the average of the square roots of the charged lepton masses (or about 1/20th of the square root of the electron mass), then the fine structure constant becomes something like 400x smaller. And the same applies to the strong force. If one redefines the coupling constants in this way, the relatively high strength of the coupling constants is attributable at least in part to the way the angle "delta" distributes mass in the Koide formula to the electron.

 

[Hans de Vries]

A question about the scalar potentials of Lienard-Wiechert. What are the two scalar values that can be used, along with their derivatives, to describe E&M fields? Or can this be done for only one source point charge at a time?

The Lienard-Wiechert formalism uses the classical 4-potential V,A. The two
scalar values I mentioned came from Ryder, and I have to correct myself
here, the paragraph that I quoted, "3.3 Complex scalar fields and the EM
field" derives the 4-current from them rather than the EM field, sorry.
Let me describe what I was hoping for:

It's interesting to have a look at the scalar fields in general which define
4-vector fields via their derivatives. In many cases this works only locally
because you get multi-valued ness globally.

For a particle one can call this scalar field the “proper age” of the particle:
The total accumulated phase during its lifetime. The derivatives in time/space
give us the energy/momentum. This scalar field can have multi-valued ness,
two paths with different “proper age” have a different accumulated phase and
the result is interference.

This “proper age” scalar field is never used because it’s not single-valued but
it is still interesting to keep in mind. There wouldn’t be any interference if it
was single valued.

The potential V can have a similar issue, a $\oint$ of E can lead to multi-valued
ness in case of induced fields. Only the combination of V and A is unique, V
by itself is not. What I was hoping for is that this could be reduced further to
two scalar fields which are unique together but multi-valued when considered
alone. I don’t know if this can be done or not but it’s kind of fundamental:
What is the minimum amount of parameters needed to describe the EM field.Regards, Hans